A projectile is launched at an angle of 30 degrees with an initial speed of 20 m

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Question: A projectile is launched at an angle of 30 degrees with an initial speed of 20 m/s. What is the maximum height reached? (g = 10 m/s²)

Options:

Correct Answer: 10 m

Solution:

Maximum height h = (u^2 * sin²θ) / (2g) = (20² * (1/2)²) / (2 * 10) = 5 m.

A projectile is launched at an angle of 30 degrees with an initial speed of 20 m/s. What is the maximum height reached? (g = 10 m/s²)

A projectile is launched at an angle of 30 degrees with an initial speed of 20 m/s. What is the maximum height reached? (g = 10 m/s²)

Step 1: Identify the given values. The initial speed (u) is 20 m/s, the angle (θ) is 30 degrees, and the acceleration due to gravity (g) is 10 m/s².
Step 2: Convert the angle from degrees to radians if necessary, but here we can use the sine value directly. For 30 degrees, sin(30°) = 1/2.
Step 3: Calculate sin²(θ). Since sin(30°) = 1/2, then sin²(30°) = (1/2)² = 1/4.
Step 4: Use the formula for maximum height: h = (u² * sin²θ) / (2g).
Step 5: Substitute the values into the formula: h = (20² * (1/4)) / (2 * 10).
Step 6: Calculate 20², which is 400. Then multiply by (1/4): 400 * (1/4) = 100.
Step 7: Calculate the denominator: 2 * 10 = 20.
Step 8: Divide the results: h = 100 / 20 = 5 m.
Step 9: Conclude that the maximum height reached by the projectile is 5 meters.

Projectile Motion – The study of the motion of an object that is launched into the air and influenced only by gravity and its initial velocity.
Maximum Height Calculation – The formula used to calculate the maximum height of a projectile based on its initial velocity and launch angle.
Trigonometric Functions – Understanding the use of sine function to resolve the vertical component of the initial velocity.